Canine Genetics Consulting
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Population Genetics and Dog Breeding

Canine Genetics Consulting Services
Liz Hare, PhD

Why is population genetics important for dog breeders? Why should you bother understanding these concepts?

As a genetics nerd and dog lover, I have lots of answers to those questions. Population genetics gives us the tools to understand how the genes for important traits behave in populations, large or small, over several generations. The concepts described here should give you a feel for how you might change the genetics of your breeding stock over time. Most of the traits that we're really interested in do not follow simple, dominant or recessive, autosomal or sex-linked inherited patterns. Rather, they are controlled by a number of genetic factors, often in combination with environmental factors. They often take on values that vary over a continuum rather than being discrete, yes-or-no, conditions: a dog's height at the withers, weight, PennHip score, running speed, or growth rate. Implementing a selection program using this kind of trait is more difficult than dealing with a trait that has a simple inheritance pattern.

It is useful, though, to develop an understanding of how single genes behave in populations. With a grasp of these concepts, it will be easier for you to understand more complex situations.

The Autosomal Dominant Case

Suppose you are faced with a condition that you want to eliminate from your population, and you know that its inheritance pattern is autosomal dominant. This is the easiest type of trait to eliminate, because you can see the dominant allele wherever it exists. If a dog has the trait you want to eliminate, he is either homozygous (and has a 100% chance of passing on the dominant disease to his or her offspring) or heterozygous (and has a 50% chance of passing the disease allele on). Ideally, you would select only parents that are homozygous recessive and don't have the condition. Hopefully, your population is large enough so that you can eliminate everyone who shows the disease, and the dominant disease allele will be gone in one short generation.

If you're dealing with a very common condition or a small population, the heterozygote might be a chance you need to take. Statistically, half of his offspring will receive the disease allele from him.

The Autosomal Recessive Case

It is much more difficult to remove a recessive disease allele from a population. You will only "see" it when it's paired up with another recessive allele. In the heterozygote, it is "hidden."

The Hardy-Weinberg Law

The Hardy-Weinberg equation describes how alleles behave in a population from generation to generation. It is an oversimplification, in that it assumes that mating is random, there is no migration in or out of the population, mutation does not occur, and there is no selection, natural or otherwise. Not very realistic, but it's a mental model to start with.

In a system with two alleles, where the frequency of p is p and the frequency of q is q, the equation states:

p2 + 2pq + q2 = 1

p2 = the frequency of the p homozygote
2pq = the frequency of the pq heterozygote. There's a 2 in front because you can get this genotype in two ways-a p from the mother and a q from the father, or a p from the father and a q from the mother.
q2 = the frequency of the q homozygote.

If p and q are equal in frequency at 0.5, then the equation looks like

0.25 + 0.5 + 0.25 = 1

If p = 0.75 and q = 0.25, it looks like

0.56 + 0.38 + 0.06 = 1

Now let's look at this kind of a situation over time. Suppose you start with a recessive trait at a frequency of 0.25, and you decide you will only breed the individuals who are free of the condition.


So, only the individuals from the p2 and 2pq columns are going to be parents in Generation 2. 0.33 are homozygotes and 0.66 are heterozygotes. The allele frequency for p is now the square root of 0.33, or 0.57. Since p + q = 1, q is now 0.43, and

2 0.330.490.18

Continuing this way (eliminating all the q2's who we know have the trait we want to eliminate), we get

3 0.40 0.47 0.13
4 0.45 0.44 0.11
5 0.51 0.41 0.08
6 0.55 0.38 0.07
7 0.60 0.35 0.05
8 0.63 0.33 0.04
9 0.68 0.29 0.03
10 0.70 0.27 0.03
11 0.72 0.26 0.02
12 0.73 0.26 0.02

Notice how, the further we go, the less the last column decreases each time. It is easier to see with a graph:

Graph with Generations on the X axis and allele frequency on the Y axis. P-squared increases in a sigmoidal curve from 0.25 to 0.75. q-squared decreases in a sigmoidal curve from 0.75 to 0.25. 2PQ decreases steadily from 0.5 to 0.26.

Now that you have seen how response to selection works at one locus, it's easier for you to expand your understanding of the genetics of complex traits.

Quantitative Genetics

Quantitative genetics looks mathematically at how complex traits are inherited. By complex, I mean that there are usually many genetic and environmental factors involved in determining the value of the trait. The trait is usually measured on a continuum, like body weight or milk production, rather than described in discrete categories, like coat color or whether a disease is present or not. We use some pretty complicated statistics to study what's going on with these kinds of traits, so I will provide a brief general introduction here.

To study continuous traits, we use statistical models, which are just mathematical equations that describe the important factors contributing to the value of a trait. These models usually assume that there are an infinite number of genes, and several environmental factors (some known and some unknown) that contribute to the variation in a trait. Because we're doing statistics, we talk about "partitioning the variance" of a trait. This means that we mathematically dissect the factors that contribute to variation in the trait.

One of the important results we get from this kind of number crunching, and one that you will see a lot in the genetics literature, is heritability. Simply stated, the heritability is the amount of variance in the trait that is due to genetic factors. It is represented as the ratio of genetic variance to total variance, where total variance is all the variance in the trait. This variance is usually considered to be due to either genetic or environmental effects (fixed and random factors like season or age) but it can also contain other terms, like dominance variance, which quantifies the variation in the trait due to the dominance interactions between alleles that affect the trait of interest.

If you think about it, most of the traits we're really interested in for dogs are quantitative traits. Some important diseases in certain breeds are simply inherited, but a lot of the other things we care about-performance in some type of work, structure (like bone size and angulation), how many puppies a bitch has-are complex traits.

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Copyright 2004 Liz Hare